Dielectrophoresis (DEP) is the motion of particles caused by the effects of conduction and dielectric polarization in non-uniform electric fields. Unlike electrophoresis, where the force acting on a particle is determined by its net charge, the dielectrophoresis force depends on the geometrical, conductive, and dielectric properties of the particle. A complex conductivity of a medium can be defined as σ*=σ+iωε, where σ is the real conductivity and ε is the permittivity of the medium, i is the square root of −1, and ω is the angular frequency of the applied electric field, E. According to well-known theory, the dielectrophoretic force is proportional to the differences in complex conductivity of the particle and suspending liquid and square of the applied electric field. Without being bound by theory, for a spherical particle of radius r, the DEP force, FDEP is given byFDEP=2πr3εmRe[fCM]∇E2 
where εm is the absolute permittivity of the suspending medium, E is the local (rms) electric field, ∇ is the del vector operator and Re[fCM] is the real part of the Clausius-Mossotti factor, defined as:
      f    CM    =                    σ        p        *            -              σ        m        *                            σ        p        *            +              2        ⁢                  σ          m          *                    
where σp* and σm* are the complex conductivities of the particle and medium respectively, as described in M. P. Hughes, et. al. Biochimica et Biophysica Acta 1425 (1998) 119-126, incorporated herein by reference. Depending on the conductivities of the particle and medium, then, the dielectrophoresis force may be positive (positive DEP), or negative (negative DEP).
Thus, when a dielectric particle is exposed to an electric field, it conducts and polarizes. The size and direction of the induced electric current and dipole depend on the frequency of the applied field and electrical properties of the particle and medium, such as conductivity, permittivity, morphology and shape of the particle. Typically in an inhomogeneous field, this causes a force due to the interaction of the induced dipole and the electric field. Particles may also be moved in electric fields due to a gradient in the field phase (typically exploited in electrorotation and traveling wave dielectrophoresis), see for example Pohl H. A., J. Appl. Phys., 22, 869-871; Pohl, H. A., Dielectrophoresis, Cambridge University Press; Huang Y., R. C. Gascoyne et al., Biophysical Journal, 73, 1118-1129; Wang X. B., Gascoyne, R. C., Anal. Chem. 71, 911-918, 1999; and U.S. Pat. No. 5,858,192, all of which are hereby incorporated by reference.
Typical devices and methods employing dielectrophoresis to manipulate particles employ electrodes shaped or arranged to generate a spatially non-uniform electric field, and therefore dielectrophoretic forces. Particles are generally drawn toward the electrode edges, or toward electric field minimums between electrode regions. This limits the particles to be manipulated to those that are compatible with the electrodes, electrode materials, electrochemical products, and sharp electric field gradients in the immediate vicinity of the electrodes.